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The supergravity (SUGRA) theories with exact global $U(1)$ symmetry or shiftsymmetry in K\"ahler potential provide the natural frameworks for inflation.However, the quadratic inflation is disfavoured by the new results onprimordial tensor fluctuations from the Planck Collaboration. To be consistentwith the new Planck data, we point out that the explicit symmetry breaking isneeded, and study these two SUGRA inflation in details. For the SUGRA inflationwith global $U(1)$ symmetry, the symmetry breaking term leads to atrigonometric modulation on inflaton potential. The coefficient of the $U(1)$symmetry breaking term is of the order $10^{-2}$, which is sufficient large toimprove the inflationary predictions while its higher order corrections arenegligible. Such models predict sizeable tensor fluctuations and highly agreewith the Planck results. In particular, the model with a linear $U(1)$ symmetrybreaking term predicts the tensor-to-scalar ratio around $\textbf{r}\sim0.01$and running spectral index $\alpha_s\sim-0.004$, which comfortably fit with thePlanck observations. For the SUGRA inflation with breaking shift symmetry, theinflaton potential is modulated by an exponential factor. The modulated linearand quadratic models are consistent with the Planck observations. In both kindsof models the tensor-to-scalar ratio can be of the order $10^{-2}$, which willbe tested by the near future observations.

Symmetry Breaking Indication for Supergravity Inflation in Light of the Planck 2015